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3 years ago

Can someone show me the work for this?

1 answer:

7 0

We are given the equation or function y = sqrt (2x + 1). The derivative of the equation is expressed as

1. dy/dt = 0.5 *2 *(2x + 1)^-0.5 dx/dt
when x = 4 and dx/dt =3
dy/dt = 0.5 *2 *3*(2*4 + 1)^-0.5
dy/dt = 1

2. dy/dt = 0.5 *2 *(2x + 1)^-0.5 dx/dt
 If dy/dt = 5, find dx/dt when x = 12.
 5= 0.5 *2 (2*12 + 1)^-0.5 dx/dt
dx/dt = 1

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Help!! Quadratic models! Will mark brainiliest!!

denis23 [38]

There seems to be a strange typo in problem 1, but I'm not sure. So I'll skip it and move onto problem 2

The answer to problem 2 is y = -0.125x^2 + 5.25x - 35.05

=======================================

Explanation:

We have the following points:

(12, 9.95) and (14, 13.95) and (16,16.95)

where x is the diameter in inches, y is the price in dollars

Use these three points to find the equation in the form y = ax^2 + bx + c

------------

Plug in (x,y) = (12,9.95). Isolate c

y = ax^2 + bx + c

9.95 = a(12)^2 + b(12) + c

9.95 = 144a + 12b + c

9.95-144a-12b = c

c = 9.95-144a-12b

------------

Plug in (x,y) = (14, 13.95)

Also, plug in c = 9.95-144a-12b

y = ax^2 + bx + c

13.95 = a(14)^2 + b(14) + c

13.95 = 196a + 14b + c

13.95 = 196a + 14b + 9.95-144a-12b

13.95 = 52a + 2b + 9.95

Solve for b

13.95 = 52a + 2b + 9.95

13.95-9.95 = 52a + 2b

4 = 52a + 2b

2b = -52a + 4

b = (-52a + 4)/2

b = -26a + 2

------------

Plug in (x,y) = (16,16.95)

y = ax^2 + bx + c

16.95 = a(16)^2 + b(16) + c

16.95 = 256a + 16b + c

Now plug in c = 9.95-144a-12b

16.95 = 256a + 16b + c

16.95 = 256a + 16b + 9.95-144a-12b

16.95 = 112a + 4b + 9.95

16.95-9.95 = 112a + 4b

7 = 112a + 4b

112a + 4b = 7

Next, plug in b = -26a+2, and solve for 'a'

112a + 4b = 7

112a + 4(-26a+2) = 7

112a + 4(-26a)+4(2) = 7

112a - 104a + 8 = 7

8a + 8 = 7

8a = 7-8

8a = -1

a = -1/8

a = -0.125

------------

Use that 'a' value to find b

b = -26a + 2

b = -26(-0.125) + 2

b = 5.25

------------

Finally, use those 'a' and 'b' values to determine c

c = 9.95-144a-12b

c = 9.95-144(-0.125)-12(5.25)

c = -35.05

------------

We found that

a = -0.125, b = 5.25, and c = -35.05

So y = ax^2 + bx + c turns into y = -0.125x^2 + 5.25x - 35.05

As a way to check the answer, we plug in the various x values to get the corresponding y values. For example, if x = 12, then

y = -0.125x^2 + 5.25x - 35.05

y = -0.125(12)^2 + 5.25(12) - 35.05

y = 9.95

Which is the proper y value we want. I'll let you check the others

7 0

3 years ago

A rectangular prism has a length of 8 inches a width of 4 inches and a height of 2 1/4 inches. The prism is filled with cubes th

Sedaia [141]

-------------------------------------------------------------------------------------
Number of 1/4 inches cubes length-wise:
-------------------------------------------------------------------------------------
$4 \div \dfrac{1}{4}$

$=4 \times 4$

$=16$

-------------------------------------------------------------------------------------
Number of 1/4 inch cubes width-wise:
-------------------------------------------------------------------------------------
$8 \div \dfrac{1}{4}$

$=8 \times 4$

$=32$

-------------------------------------------------------------------------------------
Number of 1/4 inch cubes height-wise:
-------------------------------------------------------------------------------------
$2\dfrac{1}{4} \div \dfrac{1}{4}$

$=\dfrac{9}{4} \times \dfrac{4}{1}$

$=9$

-------------------------------------------------------------------------------------
Total number of 1/4 inch cubes:
-------------------------------------------------------------------------------------
16 x 32 x 9 = 4608

-------------------------------------------------------------------------------------
Answer: 4608 cubes are needed to fill the rectangular prism
-------------------------------------------------------------------------------------

7 0

3 years ago

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5) You are buying $48 worth of peanut butter and jelly. Jelly costs $4 per jar and peanut butter costs $6

boyakko [2]

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3 years ago

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What triangle congreunce theorem could you use to prove triangle ADE is congruent to triangle CBE?

Eduardwww [97]

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